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C5×#65711 #13104471

order1600
automorphism?
homologyAbelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C2×C4

Aliases

direct productC5×#65711

Splittings

FittingC52×C4⋊C4 ⋊ C4
SylowC52 ⋊ #387

Subgroups

subgroupG/H
centerC22×C5C22×AGL(1,𝔽5)
commutatorC22×C5C22×C4×C5
FrattiniC22C22×C5×AGL(1,𝔽5)
FittingC52×C4⋊C4C4
socleC22×C52C22×C4
prime radicalC22×C5×D5C23
cosocleC22×D5C23×C5
hypercenterC5×C4⋊C4AGL(1,𝔽5)
hypocenterC5C5×#387
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C5 ◁ C5×C4⋊C4

321 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

Conjugacy classes & character table

190 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1600, 6823);